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Rolling cube footprints: number of 4Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge
1

%I #4 Mar 19 2013 07:29:05

%S 216,6912,765952,63438848,5889851392,522106961920,47175115472896,

%T 4228713130491904,380326363447427072,34157975785279848448,

%U 3069635685131267080192,275785779148632316968960

%N Rolling cube footprints: number of 4Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge

%C Row 4 of A223269

%H R. H. Hardin, <a href="/A223272/b223272.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 48*a(n-1) +4096*a(n-2) -12288*a(n-3) -1638400*a(n-4) +2097152*a(n-5) +67108864*a(n-6) for n>7

%e Some solutions for n=3

%e ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..1....0..3..1....0..3..0

%e ..0..2..1....4..2..5....0..4..0....5..4..0....1..3..4....4..2..4....5..2..0

%e ..4..2..5....1..3..5....5..3..5....2..4..5....1..3..5....4..3..5....1..3..5

%e ..4..2..4....5..2..5....5..3..5....2..4..2....5..2..0....4..2..4....4..3..4

%e Face neighbors:

%e 0.->.1.2.3.4

%e 1.->.0.2.3.5

%e 2.->.0.1.4.5

%e 3.->.0.1.4.5

%e 4.->.0.3.2.5

%e 5.->.1.3.4.2

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 19 2013